hypothesis in excel

The Complete Guide: Hypothesis Testing in Excel

In statistics, a hypothesis test is used to test some assumption about a population parameter .

There are many different types of hypothesis tests you can perform depending on the type of data you’re working with and the goal of your analysis.

This tutorial explains how to perform the following types of hypothesis tests in Excel:

• One sample t-test
• Two sample t-test
• Paired samples t-test
• One proportion z-test
• Two proportion z-test

Let’s jump in!

Example 1: One Sample t-test in Excel

A one sample t-test is used to test whether or not the mean of a population is equal to some value.

For example, suppose a botanist wants to know if the mean height of a certain species of plant is equal to 15 inches.

To test this, she collects a random sample of 12 plants and records each of their heights in inches.

She would write the hypotheses for this particular one sample t-test as follows:

• H 0 :  µ = 15
• H A :  µ ≠15

Refer to this tutorial for a step-by-step explanation of how to perform this hypothesis test in Excel.

Example 2: Two Sample t-test in Excel

A two sample t-test is used to test whether or not the means of two populations are equal.

For example, suppose researchers want to know whether or not two different species of plants have the same mean height.

To test this, they collect a random sample of 20 plants from each species and measure their heights.

The researchers would write the hypotheses for this particular two sample t-test as follows:

• H 0 :  µ 1 = µ 2
• H A :  µ 1 ≠ µ 2

Example 3: Paired Samples t-test in Excel

A paired samples t-test is used to compare the means of two samples when each observation in one sample can be paired with an observation in the other sample.

For example, suppose we want to know whether a certain study program significantly impacts student performance on a particular exam.

To test this, we have 20 students in a class take a pre-test. Then, we have each of the students participate in the study program for two weeks. Then, the students retake a post-test of similar difficulty.

We would write the hypotheses for this particular two sample t-test as follows:

• H 0 :  µ pre = µ post
• H A :  µ pre ≠ µ post

Example 4: One Proportion z-test in Excel

A  one proportion z-test  is used to compare an observed proportion to a theoretical one.

For example, suppose a phone company claims that 90% of its customers are satisfied with their service.

To test this claim, an independent researcher gathered a simple random sample of 200 customers and asked them if they are satisfied with their service.

• H 0 : p = 0.90
• H A : p ≠ 0.90

Example 5: Two Proportion z-test in Excel

A two proportion z-test is used to test for a difference between two population proportions.

For example, suppose a s uperintendent of a school district claims that the percentage of students who prefer chocolate milk over regular milk in school cafeterias is the same for school 1 and school 2.

To test this claim, an independent researcher obtains a simple random sample of 100 students from each school and surveys them about their preferences.

• H 0 : p 1 = p 2
• H A : p 1  ≠ p 2

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Excel Tutorial: How To Test Hypothesis In Excel

Introduction.

Hypothesis testing is a crucial part of data analysis, helping us make informed decisions based on statistical evidence. It allows us to determine if there is enough evidence to support or reject a claim about a population parameter. In this Excel tutorial, we will delve into the process of testing hypothesis in Excel , providing you with the knowledge and skills to confidently analyze and draw conclusions from your data.

So why is hypothesis testing so important? Well, it helps us make sense of the overwhelming amount of data we encounter in our professional and personal lives. Whether we are trying to understand consumer behavior, assess the effectiveness of a new product, or evaluate the impact of a marketing campaign, hypothesis testing allows us to make informed decisions and draw reliable conclusions.

Key Takeaways

• Hypothesis testing is essential for making informed decisions based on statistical evidence.
• Understanding null and alternative hypotheses, as well as type I and type II errors, is crucial in hypothesis testing.
• Setting up and organizing data accurately in Excel is necessary for conducting hypothesis tests.
• Interpreting the results of a hypothesis test, including determining the p-value and significance level, is important for drawing reliable conclusions.
• Avoiding common mistakes such as misinterpreting results and using the wrong test for the data is vital in hypothesis testing.

Understanding hypothesis testing

Hypothesis testing is a crucial concept in statistics that allows us to make inferences about a population based on a sample. In the context of Excel, understanding hypothesis testing is essential for data analysis and decision-making.

In hypothesis testing, the null hypothesis ( H0 ) is a statement that there is no effect or no difference in the population parameter. It is typically the hypothesis that researchers aim to refute. On the other hand, the alternative hypothesis ( Ha ) is a statement that there is an effect or a difference in the population parameter. It represents what the researchers are trying to prove.

In hypothesis testing, there are two types of errors that can occur. A Type I error occurs when the null hypothesis is rejected when it is actually true. This is also known as a false positive. A Type II error occurs when the null hypothesis is not rejected when it is actually false. This is also known as a false negative.

The significance level, often denoted as α , is the probability of rejecting the null hypothesis when it is true. In hypothesis testing, choosing the appropriate significance level is crucial as it determines the likelihood of making a Type I error. Commonly used significance levels include 0.05, 0.01, and 0.10.

Setting up the data in Excel

When conducting hypothesis testing in Excel, it is crucial to properly set up your data to ensure accurate results. Here are the key steps to follow:

The first step in testing a hypothesis in Excel is to input your data into the spreadsheet. This may include numerical values, categorical data, or any other relevant information for your analysis.

Once the data is inputted, it is important to organize it in a way that is conducive to hypothesis testing. This may involve structuring the data into relevant columns and rows, or creating separate sheets for different variables.

Prior to conducting hypothesis testing, it is essential to ensure that the data is accurate and complete. This may involve checking for any missing or erroneous values, as well as verifying the overall integrity of the dataset.

• Input all relevant data into the Excel spreadsheet.
• Organize the data in a manner that facilitates hypothesis testing.
• Verify the accuracy and completeness of the data before proceeding with hypothesis testing.

Performing a hypothesis test in Excel

When it comes to testing hypotheses in Excel, there are a few key steps to follow to ensure accurate and reliable results. Here, we'll delve into the process of performing a hypothesis test in Excel, covering everything from selecting the appropriate test for the data to interpreting the test results.

Before diving into the hypothesis testing process, it's crucial to determine the appropriate test for the data at hand. This involves understanding the nature of the data and the specific hypothesis being tested. Whether it's a t-test, chi-squared test, ANOVA, or another statistical test, choosing the right test is essential for obtaining meaningful results.

Excel offers a range of built-in functions that make hypothesis testing relatively straightforward. Functions like T.TEST, CHISQ.TEST, and ANOVA help streamline the process, allowing users to input their data and quickly obtain test statistics and p-values. Understanding how to utilize these functions is key to executing hypothesis tests accurately.

Once the hypothesis test has been run in Excel, it's important to carefully interpret the results. This involves analyzing the test statistic, p-value, and any relevant confidence intervals to determine whether the data provides enough evidence to support or reject the null hypothesis. Excel's output can provide valuable insights into the significance of the findings, helping to draw meaningful conclusions from the hypothesis test.

Interpreting the results

After conducting a hypothesis test in Excel, it is important to carefully interpret the results to draw meaningful conclusions.

Understanding the p-value

The p-value is a crucial indicator of the strength of evidence against the null hypothesis. A low p-value (typically less than 0.05) suggests that the results are statistically significant, and the null hypothesis can be rejected in favor of the alternative hypothesis.

Significance level

The significance level, often denoted as alpha (α), is the threshold at which the p-value is considered significant. Commonly used significance levels include 0.05 and 0.01.

Rejecting or failing to reject the null hypothesis

Based on the obtained p-value and significance level, it is possible to determine whether the null hypothesis should be rejected or retained. If the p-value is less than the significance level, the null hypothesis is typically rejected in favor of the alternative hypothesis.

Considering the practical significance

In addition to statistical significance, it is important to consider the practical implications of the results. Even if a hypothesis is statistically significant, it may not have meaningful real-world impact.

Interpreting the findings in context

It is essential to discuss the implications of the hypothesis test within the specific context of the research or analysis. This involves considering the broader implications and potential applications of the results.

Considering limitations and alternative explanations

Discussing the potential limitations of the hypothesis test and considering alternative explanations for the results can provide a more comprehensive understanding of the findings.

Common mistakes to avoid

When conducting hypothesis testing in Excel, it's important to be aware of common mistakes that can lead to inaccurate results. Here are some key pitfalls to watch out for:

Misinterpreting the results of hypothesis tests is a common mistake that can lead to faulty conclusions. It's important to thoroughly understand the output of the test and consider the implications of the results before drawing any conclusions.

Using the wrong hypothesis test for the type of data being analyzed can lead to incorrect results. It's essential to select the appropriate test based on the nature of the data and the research question being addressed.

Failing to check for data integrity before conducting hypothesis tests can result in unreliable results. It's crucial to ensure that the data being analyzed is accurate and free from errors or anomalies that could impact the validity of the test.

Recap: Hypothesis testing is a crucial step in data analysis as it allows us to make informed decisions based on the evidence provided by the data.

Encouragement: I highly encourage you to apply the tutorial on hypothesis testing in Excel to your own data analysis projects. It's a valuable skill that can greatly enhance the quality and reliability of your conclusions.

Final Thoughts: The significance of hypothesis testing in Excel cannot be understated. It is a powerful tool that enables us to make conclusions about the population based on sample data, ultimately leading to more accurate and meaningful insights.

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Hypothesis Test in Excel for the Population Mean (Large Sample)

Microsoft Excel for statistics > Hypothesis Test in Excel #1

Note : This article covers z-tests in Excel. If you have a small sample (under 30), or don’t know the population standard deviation , run a T Test in Excel instead.

Hypothesis Test in Excel: Overview

Hypothesis Test in Excel: Two Sample for Means

Hypothesis test in excel: manual steps.

Step 1: Type your data into a single column in Excel. For example, type your data into cells A1:A40.

Step 2: Click the “Data” tab and then click “Data Analysis.” If you don’t see the Data Analysis button then you may need to load the Data Analysis Toolpak .

Step 3: Click “ Descriptive Statistics “ and then click “OK.” When the Descriptive Statistics dialog box opens, click “Summary Statistics” and then type the location for a cell where you want your result to appear. For example, type”B1.”

Step 4: Click “OK. ” A variety of descriptive statistics, like the median and mode , will appear starting in cell B1.

Step 5: Find the cells that have the mean and the standard error results in it. If you typed in cell B1 in Step 3, your mean will be in cell C3 and your standard error will be in cell C4. Take a note of those cell locations.

Step 6: Type the following formula into cell D1 (assuming your mean is in cell C3 and your SE is in cell C4 — if they are not, you’ll need to adjust the formula): (C3-0)/C4

Change the “zero” to reflect the mean in your null hypothesis . For example, if your null hypothesis states that the mean is $7 per hour, then change the 0 to “7.”

Step 7: Press “Enter” to get the value of the test statistic. Compare the value to the accepted value for your mean from the z-table*. If the test statistic falls into the accepted range, then you will fail to reject the null hypothesis .

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#1 Excel tutorial on the net

This example teaches you how to perform a t-Test in Excel . The t-Test is used to test the null hypothesis that the means of two populations are equal.

Below you can find the study hours of 6 female students and 5 male students.

To perform a t-Test, execute the following steps.

1. First, perform an F-Test to determine if the variances of the two populations are equal. This is not the case.

2. On the Data tab, in the Analysis group, click Data Analysis.

Note: can't find the Data Analysis button? Click here to load the Analysis ToolPak add-in .

3. Select t-Test: Two-Sample Assuming Unequal Variances and click OK.

4. Click in the Variable 1 Range box and select the range A2:A7.

5. Click in the Variable 2 Range box and select the range B2:B6.

6. Click in the Hypothesized Mean Difference box and type 0 (H 0 : μ 1 - μ 2 = 0).

7. Click in the Output Range box and select cell E1.

8. Click OK.

Conclusion: We do a two-tail test (inequality). lf t Stat < -t Critical two-tail or t Stat > t Critical two-tail, we reject the null hypothesis. This is not the case, -2.365 < 1.473 < 2.365. Therefore, we do not reject the null hypothesis. The observed difference between the sample means (33 - 24.8) is not convincing enough to say that the average number of study hours between female and male students differ significantly.

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How to Do Hypothesis Tests With the Z.TEST Function in Excel

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Hypothesis tests are one of the major topics in the area of inferential statistics. There are multiple steps to conduct a hypothesis test and many of these require statistical calculations. Statistical software, such as Excel, can be used to perform hypothesis tests. We will see how the Excel function Z.TEST tests hypotheses about an unknown population mean.

Conditions and Assumptions

We begin by stating the assumptions and conditions for this type of hypothesis test. For inference about the mean we must have the following simple conditions:

• The sample is a simple random sample .
• The sample is small in size relative to the population . Typically this means that the population size is more than 20 times the size of the sample.
• The variable being studied is normally distributed.
• The population standard deviation is known.
• The population mean is unknown.

All of these conditions are unlikely to be met in practice. However, these simple conditions and the corresponding hypothesis test are sometimes encountered early in a statistics class. After learning the process of a hypothesis test, these conditions are relaxed in order to work in a more realistic setting.

Structure of the Hypothesis Test

The particular hypothesis test we consider has the following form:

• State the null and alternative hypotheses .
• Calculate the test statistic, which is a z -score.
• Calculate the p-value by using the normal distribution. In this case the p-value is the probability of obtaining at least as extreme as the observed test statistic, assuming the null hypothesis is true.
• Compare the p-value with the level of significance to determine whether to reject or fail to reject the null hypothesis.

We see that steps two and three are computationally intensive compared two steps one and four. The Z.TEST function will perform these calculations for us.

Z.TEST Function

The Z.TEST function does all of the calculations from steps two and three above. It does a majority of the number crunching for our test and returns a p-value. There are three arguments to enter into the function, each of which is separated by a comma. The following explains the three types of arguments for this function.

• The first argument for this function is an array of sample data. We must enter a range of cells that corresponds to the location of the sample data in our spreadsheet.
• The second argument is the value of μ that we are testing in our hypotheses. So if our null hypothesis is H 0 : μ = 5, then we would enter a 5 for the second argument.
• The third argument is the value of the known population standard deviation. Excel treats this as an optional argument

Notes and Warnings

There are a few things that should be noted about this function:

• The p-value that is output from the function is one-sided. If we are conducting a two-sided test, then this value must be doubled.
• The one-sided p-value output from the function assumes that the sample mean is greater than the value of μ we are testing against. If the sample mean is less than the value of the second argument, then we must subtract the output of the function from 1 to get the true p-value of our test.
• The final argument for the population standard deviation is optional. If this is not entered, then this value is automatically replaced in Excel’s calculations by the sample standard deviation. When this is done, theoretically a t-test should be used instead.

We suppose that the following data are from a simple random sample of a normally distributed population of unknown mean and standard deviation of 3:

1, 2, 3, 3, 4, 4, 8, 10, 12

With a 10% level of significance we wish to test the hypothesis that the sample data are from a population with mean greater than 5. More formally, we have the following hypotheses:

• H 0 : μ= 5
• H a : μ > 5

We use Z.TEST in Excel to find the p-value for this hypothesis test.

• Enter the data into a column in Excel. Suppose this is from cell A1 to A9
• Into another cell enter =Z.TEST(A1:A9,5,3)
• The result is 0.41207.
• Since our p-value exceeds 10%, we fail to reject the null hypothesis.

The Z.TEST function can be used for lower tailed tests and two tailed tests as well. However the result is not as automatic as it was in this case. Please see here for other examples of using this function.

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Hypothesis Testing in Excel

Hypothesis t-Test Testing using T.Test Excel function

To test t test hypotesis in Excel you can just use T.Test function. The syntax of T.TEST Excel function:

• Array1: the first set of data to test
• Array2: the second set of data to test
• Tails: the number of tails where 1. is one-tailed distribution and 2 is for two tailed distribution
• Type: 1 is for paired, 2 for homoscedastic, 3 for heteroscedastic

This is the data set and two arrays for my t hypothesis. I’d like to test the hypothesis if the is a difference in given arrays.

The formula I used for T-Test hypothesis is

=T.TEST($B$2:$B$6,$C$2:$C$8,1,3)

because the variance  of these arrays is different.

Now we need to interpret the calculated probability . Calculated p ≥ 0.05 means that difference is not significant and p ≤ 0.05 means that difference is significant. The hypothesis result is 0.406325 so the difference is not significant.

Hypothesis T-Test Testing using Analysis Toolpak Add-in

There is also a possibility to perform the same t hypothesis testing using Analysis Toolpak Add-in.

1. Click on Data on the top, beside formula.

2. Click Data analysis.

Note: The data analysis is quite standard. But if it does not show under the data, then it is more likely that it has not been added, which could be done by clicking on File > Options > Add-Ins > Clicking Go on the down side when manage shows Excel Add-ins, and then choosing Data Analysis, and it will be ready.

3. Browse the Data Analysis, and choose the t-text: two-sample assuming unequal variances (1), and press ok (2).

4. Select the data for the two columns (1), write 0 in the Hypothesized mean difference (2), select the cell desired in the output range (3), and press ok (4).

And this is how to handle Hypothesis Testing in Excel.

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How to Test Hypothesis in Excel

In this Excel tutorial, you will learn how to test hypothesis in Excel application based on given data arrays. This is a testing that make it possible to test if two range are equal to one another.

Table of Contents

Hypothesis t-Test Testing using T.Test Excel function

To test t test hypotesis in Excel you can just use T.Test function.

The syntax of T.TEST Excel function:

• Array1: the first set of data to test
• Array2: the second set of data to test
• Tails: the number of tails where 1. is one-tailed distribution and 2 is for two tailed distribution
• Type: 1 is for paired, 2 for homoscedastic, 3 for heteroscedastic

This is the data set and two arrays for my t hypothesis. I’d like to test the hypothesis if the is a difference in given arrays.

The formula I used for ttest hypothesis is  =T.TEST($B$2:$B$6,$C$2:$C$8,1,3) because the variance  of these arrays is different.

Interpret the results of your hypothesis test in the context of your research question. Explain what the results mean and how they support or refute your hypothesis. To do that you need to interpret the calculated probability . Calculated p ≥ 0.05 means that difference is not significant and p ≤ 0.05 means that difference is significant. The hypotesis result is 0.406325 so the difference is not significant.

Hypothesized difference has been calculated but let’s check one more method with an add-in.

Hypothesis t-Test Testing using Analysis Toolpak Add-in

There is also a possibility to perform the same t hypothesis testing using Analysis Toolpak Add-in.

Click on Data on the top, beside formula. Click Data analysis.

Note: The data analysis is quite standard. But if it does not show under the data, then it is more likely that it has not been added, which could be done by clicking on File > Options > Add-Ins > Clicking Go on the down side when manage shows Excel Add-ins, and then choosing Data Analysis, and it will be ready.

Browse the Data Analysis, and choose the t-text: two-sample assuming unequal variances.

Select the data for the two columns, write 0 in the Hypothesized mean difference, select the cell desired in the output range.

And this is how to handle Hypothesis Testing in Excel.

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How to Do a T Test in Excel (2 Ways with Interpretation of Results)

Download the Practice Workbook

T Test.xlsx

T Test Types

There are two types of t-tests. They are:

• One-tailed t-test
• Two-tailed t-test

Each of them has 3 subtypes. They are:

• Two sample equal variance
• Two sample unequal variance

How to Do a T-Test in Excel: 2 Effective Ways

Method 1 – using the excel t.test or ttest function for a t-test, case 1.1 – two sample equal variance t-test.

In the dataset, you will see the prices of different laptops and smartphones. Here is a formula that performs a T-Test on the prices of these products and returns the t-test result.

=T.TEST(B5:B14,C5:C14,2,2)

We set the 3rd argument of the function to 2 as we are doing a two-tailed t-test on the dataset. The 4th argument should be 2 for a two-sample equal variance t-test.

Case 1.2 – Paired T-Test

We are going to apply another formula to calculate the Paired T-Test . The following dataset shows the performance mark of some employees in two different criteria.

=T.TEST(C5:C13,D5:D13,2,1)

Note: The explanation of the results is described in the following sections.

Method 2 – Using the Analysis ToolPak

• Go to the Options window.
• Select Add-ins and click on the Go button in the Manage section.

• The Add-ins window will appear. Select Analysis ToolPak and click OK again.

Case 2.1 – Tw-Sample Equal Variance T-Test

• Click on the Data Analysis button from the ribbon of the Data tab.
• The Data Analysis features will appear. Select t-Test: Two Sample Assuming Equal Variances and click OK .

• Set up the parameters for the t-test operation. Insert the Laptop and Smartphone prices as Variable 1 Range and Variable 2 Range. Include the headings in the range and check Labels.
• Set the value of Hypothesized Mean Difference to 0 .
• Select an Output option of your preference and click OK .

• As we have chosen a New Worksheet for the outputs, we will see the results in a new sheet.

Comments on Results

The output shows that the mean values for Laptops and Smartphones are 1608.85 and 1409.164 respectively. We can see from the Variances row that they are not precisely equal, but they are close enough to be assumed to have equal variances. The most relevant metric is the p-value .

The difference between means is statistically significant if the p-value is less than your significance level. Excel calculates p-values for one- and two-tailed T Tests .

One-tailed T Tests can detect only one direction of difference between means. A one-tailed test, for example, might only evaluate whether Smartphones have higher prices than Laptops . Two-tailed tests can reveal differences that are larger or smaller than. There are some other disadvantages to utilizing one-tailed testing, so I’ll continue with the conventional two-tailed results.

For our results, we’ll utilize P(T=t) two-tail, which is the p-value for the t-test’s two-tailed version. We cannot reject the null hypothesis because our p-value ( 0.095639932 ) is greater than the conventional significance level of 0.05 . The hypothesis that the population means differ is supported by our sample data. The mean price of Laptops is greater than the mean price of Smartphones’ .

The Analysis ToolPak also returns results for a one-tailed t-test . Here, the one-tailed P value of the two-sample equal variance t-test is 1.734 .

Case 2.2 – Paired T-Test

Select the t-Test: Paired Two Samples for Mean when you open the Data Analysis window.

The result shows that the mean for the Workpace is 104 and the mean for the Efficiency is 96.56 .

The difference between means is statistically significant if the p-value is less than your significance level. For our results, we’ll utilize P(T=t) two-tail, which is the p-value for the t-test’s two-tailed version. We cannot reject the null hypothesis because our p-value ( 0.188 ) is greater than the conventional significance level of 0.05 . The hypothesis that the population means differ is supported by our sample data. In particular, the Workpace mean exceeds the Efficiency mean.

How to Interpret T-Test Results in Excel

Let’s bring out the results again.

• The mean of laptop prices = 1608.85
• The mean of smartphone prices = 1409.164

ii. Variance

• The variance of laptop prices = 77622.597
• The variance of smartphone prices = 51313.7904

iii. Observations

The number of observations for both laptops and smartphones are 10 .

iv. Pooled Variance

The samples’ average variance, calculated by pooling the variances of each sample.

The mathematical formula for this parameter is:

((No of observations of Sample 1-1)*(Variance of Sample 1) + (No of observations of Sample 2-1)*(Variance of Sample 2))/(No of observations of Sample 1 + No of observations of Sample 2 – 2)

So it becomes: ((10-1)*77622.59676+(10-1)*51313.7904)/(10+10-2) = 64468.19358

v. Hypothesized Mean Difference

We “hypothesize” that the number is the difference between the two population means. In this situation, we chose 0 because we want to see if the difference between the means of the two populations is zero.

It indicates the value of the Degrees of Freedom. Formula for this parameter is:

No of observations of Sample 1 + No of observations of Sample 2 – 2 = 10 + 10 – 2 = 18

vii. t-Stat

The test statistic value of the t-Test operation.

The formula for this parameter is given below.

(Mean of Sample 1 – Mean of Sample 2)/(Square root of (Pooling Variance* (1/No of observations of Sample 1 + 1/No of observations of Sample 2)))

So it becomes: (1608.85 – 1409.164)/Sqrt(64468.19358 * (1/10 + 1/10)) = 1.758570846

viii. P(T<=t) two-tail

A two-tailed t-test’s p-value. This value can be found by entering t = 1.758570846 with 18 degrees of freedom into any T Score to P Value Calculator.

In this situation, the value of p is 0.095639932 . Because this is greater than 0.05 , we cannot reject the null hypothesis. This suggests that we lack adequate evidence to conclude that the two population means differ.

ix. t-Critical two-tail

This is the test’s crucial value. A t-Critical value Calculator with 18 degrees of freedom and a 95% confidence level can be used to calculate this number.

In this instance, the critical value is 2.10092204 . We cannot reject the null hypothesis because our test statistic t is less than this number. Again, we lack adequate information to conclude that the two population means are distinct.

Things to Remember

• Excel demands that your data be arranged in columns, with data from each group in a separate column. The first row should have labels or headers.
• Clearly state your null hypothesis (usually that there is no significant difference between the group means) and your alternative hypothesis (the opposite of the null hypothesis).
• As a result of the t-test, Excel returns the p-value. A small p-value (usually less than the specified alpha level) indicates that the null hypothesis may be rejected and that there is a substantial difference between the group means.

Frequently Asked Questions

Can I perform a t-test on unequal sample sizes in Excel?

Yes, you can use the T.TEST function to do a t-test on unequal sample sizes. When calculating the test statistic, Excel automatically accounts for unequal sample sizes.

What is the difference between a one-tailed and a two-tailed t-test?

A one-tailed t-test determines if the means of the two groups differ substantially in a given direction (e.g., greater or smaller). A two-tailed t-test looks for any significant difference, regardless of direction.

Can I calculate the effect size in Excel for t-tests?

While there is no built-in tool in Excel to calculate effect size, you can manually compute Cohen’s d for independent t-tests and paired sample correlations for paired t-tests using Excel’s basic mathematical operations.

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Statistics By Jim

Making statistics intuitive

How to Test Variances in Excel

By Jim Frost 7 Comments

Use a variances test to determine whether the variability of two groups differs. In this post, we’ll work through a two-sample variances test that Excel provides. Even if Excel isn’t your primary statistical software, this post provides an excellent introduction to variance tests. Excel refers to this analysis as F-Test Two-Sample for Variances.

In this post, I provide step-by-step instructions for using Excel to conduct a two-sample variance test and interpreting the statistical results. I also include links to supplementary information I’ve written.

Before proceeding, ensure that Excel’s Data Analysis ToolPak is installed for Excel. Look for Data Analysis as shown below.

If you don’t see Data Analysis, you’ll have to install that ToolPak. Learn how to install it in my post about using Excel to perform t-tests . It’s free!

F-test for Two-Sample Variances in Excel

In general, variances tests assess the variability of the data in multiple groups to determine whether they are different. Variance is a measure of variability that uses squared units, which makes it hard for us humans to interpret. However, various statistical procedures include variances in their calculations. The standard deviation is a more common measure of variability, and it is simply the square root of the variance. Standard deviations are much easier to interpret because they use the same units as the original data.

Analysts frequently use F-tests to assess the differences between group means in analysis of variance (ANOVA) . However, F-tests are very flexible tests that evaluate the ratio of two variances. By changing the variances in the numerator and denominator, analysts can use F-tests to assess a diverse array of properties, such as the overall statistical significance of a regression model to the differences between group means. For variance tests, we’ll use the F-test to determine whether two variances are different.

Excel can perform only two-sample variance tests, which assesses variances for precisely two groups. However, other types of tests can compare variability for more groups.

Typically, you perform this hypothesis test to determine whether two population variances are different. This form of the test uses independent samples. In other words, each group contains different people or items.

From Excel’s Data Analysis popup, choose F-test Two-Sample for Variances .

Related post : Measures of Variability

Hypotheses in Variances Tests

The standard two-tailed two-sample variance tests use the following hypotheses:

• Null : The two population variances are equal.
• Alternative : The two population variances are not equal.

If the p-value is less than your significance level (e.g., 0.05), you can reject the null hypothesis. The difference between the two variances is statistically significant. This condition indicates that your sample provides strong enough evidence to conclude that the variability in the two populations are different. In other words, their spreads differ. Hypothesis tests, like variance tests, allow you to use samples to draw conclusions about populations.

Unfortunately, Excel provides a p-value for only the one-tailed form of the variances test. One-tailed tests can detect differences between means in only one direction. For example, a one-tailed test might determine only whether Group A’s variability is greater than Group B’s variability. Two-tailed tests can detect differences in either direction—greater than or less than. There are additional drawbacks to using one-tailed tests. I wish Excel provided both one-tailed and two-tailed results as it does with two-sample t-tests.

Related posts : Hypothesis Testing Overview and One and Two-Tailed Hypothesis Tests

Performing the Two-Sample Variances Test in Excel

For this example, I’ll use data from my blog post about a Mythbusters’ Battle of the Sexes episode . In that episode, the Mythbusters evaluate whether men or women are better at parallel parking.

The Mythbusters have ten subjects per group and use a parking test that produces scores between 0 and 100. The mean difference between men and women is not statistically significant.

However, while testing the subjects, the hosts noticed that the women’s parallel parking skills appear to be more variable than the men’s abilities. The graph below shows how women have a broader range of scores than men.

While the spread of these two groups looks very different, let’s use Excel’s variances test to determine whether this difference is statistically significant.

To perform a two-sample variance test in Excel, arrange your data in two columns, as shown below. Download the CSV file that contains the data for this example: VariancesTest .

• In Excel, click Data Analysis on the Data tab.
• From the Data Analysis popup, choose F-Test Two-Sample for Variances .
• Under Input , select the ranges for both Variable 1 Range and Variable 2 Range .
• Check the Labels checkbox if you have meaningful variable names in row 1. This option makes the output easier to interpret. Ensure that you include the label row in step #3.
• Excel uses the default Alpha value of 0.05, which you usually won’t need to change. Alpha is also known as the significance level.

For this example, the popup should look like the following:

After Excel creates the statistical output, I autofit column A to display all of it.

Interpreting the Test Results

The output indicates that the variance for Males is 131.3778, and for Females it is 982.2778. The difference between these numerical measures of variances corresponds to the difference we observed in the graph. The p-value is the most important statistic. If you want to learn about the other statistics , read my posts about F (i.e., the F-value) , df (degrees of freedom) , and critical values .

For our results, we’ll use the P(F<=f) one-tail row, which is the p-value for the one-tailed form of the variances test. Because our p-value (0.003094) is less than the standard significance level of 0.05, we can reject the null hypothesis. Our sample data support the hypothesis that the population variances are different. Women are more variable at parallel parking than men.

What Excel’s Variances Test Does Not Include

Excel’s only variances test is the F-test. F-tests can assess only two groups and are susceptible to departures from normality . However, other two-sample tests are less sensitive to departures from normality, such as Bonett’s and Levene’s tests. Levene’s test is particularly suitable for small samples (>20) and skewed data.

If you have more than two groups, use Bartlett’s or Levene’s test to evaluate their variances. Bartlett’s test is more sensitive to the normality assumption than Levene’s test.

As I mentioned earlier, Excel, strangely, only offers the one-tailed test result, which is often inappropriate.

Finally, it would be nice if Excel converted the variances to standard deviations and displayed confidence intervals. The variances that Excel displays are not intuitive. Additionally, they are only the point estimates from the samples. Confidence intervals help you determine a range of values that the population parameter is like to fall within.

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Reader Interactions

May 10, 2021 at 9:38 pm

It appears that Excel 2016 calculates the F test for two tails.

April 19, 2021 at 2:22 pm

Thank you for your explanation of Excel’s F-test for equal variances. However, there is an issue with Excel’s calculation that I was recently made aware of by one of my students. If you note in your results table, the observed F-value (0.13) is smaller than the critical F-value (0.31), but the p-value is quite small (0.003).

Excel recommends that the group with the larger variance be selected as the first group (or first column) and the other group with smaller variance selected as the second column data. This would provide F-calculations that are more consistent with p-values.

April 19, 2021 at 3:40 pm

February 28, 2021 at 3:13 pm

Thank you for some fantastic books, introducing myself and others to the magical world of statistics!

I have a question that I hope you can help me with. The statistical software I use, do not have a function for Bonett Hypothesis test, why I thought I would create one. So far, I’ve done the calculations for the confidence interval and they are spot on (when I use the data you provide in your hypothesis book at page 238 and compare the Bonett confidence interval-result to my own).

However, I can’t seem to figure out how to calculate the p-value. I’ve found documentation at minitab.coms webpage, https://support.minitab.com/en-us/minitab/20/help-and-how-to/statistics/basic-statistics/how-to/1-variance/methods-and-formulas/methods-and-formulas/#hypothesis-test-for-the-chi-square-method , for how to calculate the p-value, but I’m still unsure how it is done, since the equation to solve for alpha contains inverse cumulative probability.

Can you help me out here?

Thanks in advance and thank you for some really good books!

November 24, 2019 at 1:23 am

I liked it very much

November 19, 2019 at 5:48 pm

Valuable informations

November 18, 2019 at 3:51 am

very interesting and important

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Home » Statistical Analysis Excel » Hypothesis Testing

Struggling with Hypothesis Testing in Excel?

Qi macros makes hypothesis testing easy, even if you don't know anything about statistics.

Run Any Hypothesis Test using QI Macros

• Select your data.
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What is a Hypothesis Test?

A hypothesis test helps identify ways to reduce costs and improve quality. Hypothesis testing asks the question: Are two or more sets of data the same or different, statistically.

For companies working to improve operations, hypothesis tests help identify differences between machines, formulas, raw materials, etc. and whether the differences are statistically significant or not. Without such testing, teams can run around changing machine settings, formulas and so on causing more variation. These knee-jerk responses can amplify variation and cause more problems than doing nothing at all.

Three Types of Hypothesis Tests

• Classical Method - comparing a test statistic to a critical value
• p Value Method - the probability of a test statistic being contrary to the null hypothesis
• Confidence Interval Method - is the test statistic between or outside of the confidence interval

How to Conduct a Hypothesis Test

• Define the  null (H0) and an alternate (Ha) hypothesis .
• Conduct the test.
• Calculate the test statistic and the critical value (t-Test, F-test, z-Test, ANOVA, etc.).
• Calculate a p value and compare it to a significance level (a) or confidence level (1-a).
• Interpret the results to determine if you "cannot reject null hypothesis (accept null hypothesis)" or "reject the null hypothesis."

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